Eigenvalues of non-Hermitian Fibonacci Hamiltonians

We study, using numerical methods, the effects of a non-Hermitian field h on the eigenvalues of a tight-binding Fibonacci system. For vanishing non-Hermitian field, all eigenvalues are real and correspond to critical eigenfunctions. The eigenvalues become complex and eigenfunctions tend to be delocalized for non-zero values of the parameter h. The transition from critical to extended states is monitored through the inverse participation ratio as a function of h. A simple two-band model is introduced to explain the behavior of the eigenvalues on the complex plane. (C) 2001 Elsevier Science B.V. All rights reserved.